The problem of estimating the number of all possible multiple short circuit faults in a network with a given number of lines is settled in this correspondence. A new combinatorial number, namely an associated Bell number B'(r), which enumerates the number of possible partitions of a set {1, 2,???, r} with certain constraints, is introduced. This concept immediately resolves the counting problem of short-circuit or bridging faults in an electrical network. A related combinatorial problem is also discussed which shows that under some realistic model of circuit failure, the number of possible ways the network can malfunction is closely connected to the Fibonacci sequence.